Wright functions of the second kind and Whittaker functions

In the framework of higher transcendental functions, the Wright functions of the second kind have increased their relevance resulting from their applications in probability theory and, in particular, in fractional diffusion processes. Here, these functions are compared with the well-known Whittaker...

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Bibliographic Details
Published inFractional calculus & applied analysis Vol. 25; no. 3; pp. 858 - 875
Main Authors Mainardi, Francesco, Paris, Richard B., Consiglio, Armando
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2022
Subjects
Abstract Harmonic Analysis
Analysis
Functional Analysis
Integral Transforms
Mathematics
Mathematics and Statistics
Operational Calculus
Original Paper
Wright functions
Hypergeometric functions
30B10
26A33 (primary )
33C20
Whittaker functions
30E15
41A60
Laplace transform
Fractional calculus
34E05
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Summary:In the framework of higher transcendental functions, the Wright functions of the second kind have increased their relevance resulting from their applications in probability theory and, in particular, in fractional diffusion processes. Here, these functions are compared with the well-known Whittaker functions in some special cases of fractional order. In addition, we point out two erroneous representations in the literature.
ISSN:1311-0454
1314-2224
DOI:10.1007/s13540-022-00042-2